Among the many problems arising from cell biology and medicine, shape phenotype mapping (the detailed measurement of shape related quantities from cells and subcellular organelles) from microscopy images has received particular attention in the past due to its relevance to numerous biological processes. We aim to make a fundamental contribution to cellular and subcellular phenotype mapping by developing methods for recover the underlying articulation parameters (deformation modes) of distribution of forms with particular relevance to cell biology. More specifically, we will couple a metric space formulation for biological forms with modern nonlinear manifold learning algorithms for characterizing (determination of mean shape, most likely modes of variation, statistical tests, etc.) shape distributions directly and automatically from image data. A particular innovative aspect of our work will be in allowing for using existing data to guide in the design of statistical tests to differentiate populations of cells (or subcellular organelles). These should allow for more sensitive statistical tests as compared with traditional approaches which are based on testing pre-conceived hypothesis. The methods we propose will be compared to already existing works in an effort to produce a standard, well-accepted technology. The successful completion of this project will have significant impact in areas such as pathology, high-throughput screening, cell motility studies, etc. by enabling one to perform many intricate tasks using a standard methodology. PUBLIC HEALTH RELEVANCE: This research is aimed at supporting high-throughput shape phenotype mapping automatically from microscopic images through the introduction of a rigorous mathematical foundation, accompanied by suitable computational algorithms. More specifically, we will develop methodology for performing high-level shape measurements (determination of mean shape, most likely modes of variation, statistical tests, etc.) based on the spatial transformations that relate two or more forms as depicted in microscopy images. The methods we propose will be compared to already existing works in an effort to produce a standard, well-accepted technology. The successful completion of this project will have significant impact in areas such as pathology, high-throughput screening, cell motility studies, etc. by enabling one to perform many intricate tasks using a standard methodology.